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在[[数学]]与[[物理学]]中，'''辛向量场'''（{{lang|en|symplectic vector field}}）是[[流 (数学)|流]]保持[[辛形式]]的[[向量场]]。即如果 <math>(M,\omega)</math>… {{geometry-stub}} …

…ectic''' ('''Marsden–Weinstein''') '''quotients'''，以及[[symplectic cut]]s和[[symplectic sum|sums]]。 == Symplectic quotients == …

{{General geometry}} …/20220129051827/https://www.quantamagazine.org/the-fight-to-fix-symplectic-geometry-20170209 |dead-url=no }}</ref> …

一个泊松流形可以分成一族'''辛叶子'''（{{lang|en|symplectic leaves}}）。每一片叶子是泊松流形的一个子流形，每片叶子自身是一个辛流形。两个点在同一片叶子上如果他们由一个哈密顿向量场的[[积分曲线]]连接。 * V. Guillemin, S. Sternberg, ''Symplectic Techniques in Physics'', Cambridge Univ. Press 1984. …

* Dusa McDuff and D. Salamon: ''Introduction to Symplectic Topology'' (1998) Oxford Mathematical Monographs, ISBN 0-19-850451-9. * Gromov, M. Pseudoholomorphic curves in symplectic manifolds. Invent. Math. 82 (1985), no. 2, 307--347. …

…s://web.archive.org/web/20230520204522/https://math.mit.edu/~cohn/Thoughts/symplectic.html |dead-url=no }}</ref>因此需要线性映射<math>TM \rightarrow T^*M </math>，从[[切丛|切 …name="Gosson">{{cite book |first=Maurice |last=de Gosson |title=Symplectic Geometry and Quantum Mechanics |year=2006 |publisher=Birkhäuser Verlag |location=Bas …

[[数学]]上，'''切触几何'''({{lang-en|Contact geometry}})是研究[[流形]]上的''完全不可积''超平面的几何。根据[[弗洛比尼斯定理]]，这个（大致来讲）可以通过[[叶状结构]]的不成立来识别。作为它的 …統]]<ref>A. Sergyeyev, New integrable (3+1)-dimensional systems and contact geometry, Lett. Math. Phys. 108 (2018), no. 2, 359-376 {{doi|10.1007/s11005-017-1013 …

…flavoured overview of Gromov–Witten invariants and quantum cohomology for symplectic manifolds, very technically complete …logy |editor-first=C. B. |editor-last=Thomas |title=Contact and Symplectic Geometry |url=https://archive.org/details/contactsymplecti00thom |url-access=limited …

* McDuff, Dusa & Salamon, Dietmar (2004). ''J-Holomorphic Curves and Symplectic Topology'', American Mathematical Society colloquium publications. {{isbn|0 …ry and quantum cohomology. In C. B. Thomas (Ed.), ''Contact and Symplectic Geometry'', pp.&nbsp;171–200. Cambridge University Press. {{isbn|0-521-57086-7}} …

…ichael S. |last2=Holm |first2=Darryl D.| last3=Tronci|first3=Cesare |title=Geometry of Nonadiabatic Quantum Hydrodynamics |journal=Acta Applicandae Mathematica …78-94-009-3807-6| url-access=registration| url=https://archive.org/details/symplecticgeomet0000libe}} …

* {{cite book|last=Sternberg|title=Lectures on Differential Geometry|first=Shlomo|publisher=Prentice Hall|year=1964}} * {{cite book|author=McDuff, D. and Salamon, D.|title=Introduction to Symplectic Topology|publisher=Oxford University Press|year=1998|id=ISBN 0-19-850451-9} …

…ath>\; (C^{\infty}(M),\bullet,\Delta)\; </math>形成一个BV代数，参见<ref>A. Schwarz, Geometry of Batalin-Vilkovisky quantization, arxiv: hep-th/9205088</ref><ref>D. Fior …

…thor=Griffiths, Phillip and Harris, Joseph | title=Principles of Algebraic Geometry | *{{cite book | author=Hartshorne, Robin | title=Algebraic Geometry | …

…rst=Theodore|title=The Geometry of Physics|url=https://archive.org/details/geometryofphysic0000fran|publisher=Cambridge University Press|location=Cambridge|yea …st=Dusa|coauthors=Salamon, D.|authorlink=Dusa McDuff|title=Introduction to Symplectic Topology|series=Oxford Mathematical Monographs||year=1998|isbn=0-19-850451- …

|title=Introduction to Symplectic Topology …r |first=Andreas |last=Floer |title=The unregularized gradient flow of the symplectic action |url=https://archive.org/details/sim_communications-on-pure-and-appl …

…uthor-link2=Alan Weinstein|date=2008|chapter=Group-like objects in Poisson geometry and algebra |series=Contemporary Mathematics |url=http://www.ams.org/conm/4 …sg/content/vols/0009/0003/a002/abstract.php |journal=Journal of Symplectic Geometry |language=EN |volume=9 |issue=3 |pages=285–341 |arxiv=math/0605694 |doi=10. …

微分幾何（differential geometry）作為一個獨特的學科的出現一般歸功於[[高斯]]（Carl Friedrich Gauss）和[[黎曼]]（ Bernhard Riemann）。黎曼在 …似的流形是均勻的。在[[漢密爾頓力學]]中作為相位空間出現的反切叢（Cotangent bundles）是激勵的例子，但是許多緊湊型流形也具有扭對稱（symplectic）結構。 …

#越来越多的辛几何特别是[[辛场论]](symplectic field theory)的研究者发现，辛场论和弦拓扑的研究对象有类似之处，那么这两者之间到底有什么关系？ …field theory interpreted in classical algebraic topology'', in ''Topology, geometry and quantum field theory'', 344-357, London Math. Soc. Lecture Note Ser.,… …

…'[http://www.springerlink.com/content/hq3au3baggr3/ Lectures on Symplectic Geometry]{{Dead link|date=2020年2月 |bot=InternetArchiveBot |fix-attempted=yes }}'',… …

| ''J-holomorphic Curves and Symplectic Topology''（譯：《[[擬全純曲線]]和[[扭對稱拓樸學]]》） (AMS Colloquium Publications, 52, 初版… | ''Positivity in [[代數幾何|Algebraic Geometry]] I and II'', 2004 …